Hi!
I’m having trouble to create conic-corner-cubes with perfect curvature.
I used “rounded rectangle - conic corners” and “rail revolve” to create a few rounded cubes in-between a sphere and a cube. The curvature of faces parallel to the revolving axis (as shown in front view) looks perfectly smooth; but the curvature of faces perpendicular to the revolving axis (as shown in top view) has sharp turns. In rendering mode, it looks slightly edged.
Is there a way to create these cubes with perfectly smooth curvature at all faces? Thanks!

I think this is maybe a step back from what you want, but it’s how I made a curved cube. Perhaps my approach can spark a better way. I cut away a square section from a sphere to make the faces of my cube. Bring the faces mid points together and trim them, then use variable radius fillet.

After starting to write this I realised the quicker way to make the cube is to use six spheres and boolean split them. That leaves you a central cube that is perfectly trimmed. That is the cube with zebra stripping below with radius edges.

Wow, it’s really interesting to think of a curved cube with six spheres!
I’ll try creating some conic curved bodies first, then place and boolean split them.
I’m a little obsessed with all kinds of conic curves recently haha.
Thank you for the inspiration, Bill!

The conic corners have identical rho (a parameter of conic curves. If it’s 0.5, it’s parabola; larger than 0.5, hyperbola; smaller than 0.5, ellipse) and tangent in the mid point of the cube faces. So boolean seems won’t lead me to these corners.
I tried “Blend” yesterday, but it has a different parameter, so that though it can continue the curvature, it won’t keep the conic rho, unless I know how to translate and equal these two different parameters.
A bit OCD here lol… Grasshopper may do the job?